In the field of petroleum well drilling and logging, resistivity logging tools are frequently used to provide an indication of the electrical resistivity of rock formations surrounding an earth borehole. (Such information regarding resistivity is useful in ascertaining the presence or absence of hydrocarbons.) A typical electromagnetic resistivity logging tool includes a transmitter antenna and multiple receiver antennas located at different distances from the transmitter antenna along the axis of the tool. The transmitter antenna creates electromagnetic fields in the surrounding formation, which in turn induce a voltage in each receiver antenna. Due to geometric spreading and absorption by the surrounding earth formation, the induced voltages in the receiving antennas have different phases and amplitudes.
Experiments have shown that the phase difference (D) and amplitude ratio (attenuation, A) of the induced voltages from any two receiver antennas are indicative of the resistivity of the formation. The depth of investigation (as defined by an averaged radial distance from the tool axis) to which such a resistivity measurement pertains is a function of the frequency of the transmitter and the distance from the transmitter to the mid-point between the two receivers. Thus, one may achieve multiple radial depths of investigation of resistivity either by providing multiple transmitters at different distances from the receiver pair or by operating a single transmitter at multiple frequencies, or both.
Many formations are electrically anisotropic, a property which is generally attributable to fine layering during the sedimentary build-up of the formation. Hence, in a formation coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities Rx and Ry in directions x and y, respectively, are the same, but resistivity Rz in the z direction may be different from Rx and Ry. Thus, the resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is known as the horizontal resistivity, Rh, and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is known as the vertical resistivity, Rv. One measure of formation anisotropy is the index of anisotropy, which is defined as η=[Rv/Rh]1/2.
The relative dip angle, θ, is the angle between the tool axis and the normal to the plane of the formation. Resistivity anisotropy and relative dip angle each have significant effects on resistivity logging tool measurements. As a result, resistivity logging systems should account for formation anisotropy and relative dip if accurate resistivity logs are to be obtained. To facilitate the determination of the anisotropic resistivity parameters (Rh, Rv, and θ), at least one of the transmit or receive antennas is tilted or oriented transversely to the tool axis to introduce an azimuthal sensitivity, and in practice it is becoming common to configure multiple ones of the transmitter and receiver antennas as multi-component antennas. Moreover, at least some multi-component resistivity logging systems also acquire measurements using multiple signal frequencies.
Often, an inversion process is employed to derive the formation parameters from the resistivity tool measurements. In an inversion process, the tool measurements are compared to synthetic measurements derived from a parameterized formation model, and the model parameters are adjusted until the synthetic measurements match the tool measurements. Though the increased number of measurements offered by multi-spacing, multi-frequency, and multi-component logging tools creates the potential for increased model complexity and improved characterization accuracy, the large parameter space associated with unduly complex models renders them computationally infeasible and prone to numerical errors from unnecessary parameters.
Thus, when the existing inversion processes fail to accurately characterize certain formations, it is often unwise to pursue the conventional approach of merely increasing the number of model parameters and/or increasing the number of measurements being operated on by the inversion process. Rather, a more selective approach is called for.
It should be understood, however, that the specific embodiments given in the drawings and detailed description thereto do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and modifications that are encompassed together with one or more of the given embodiments in the scope of the appended claims.